Some Elementary Combinatorial Properties of Aktas' Soft Groups with Contributions in Soft Actions

A. Pouhassani, H. Doostie, H. Rasouli

Abstract


As a generic mathematical tool, the concept of soft sets introduced in 1999 by Molodtesov, and in continuation of this research the soft groups defined and studied for their nice properties by Aktas in 2007. Because of the extensive applications of soft sets and soft groups in all branches of sciences involving mathematics we prefer to concentrate on the algebraic properties of algebraic structures. The action of groups on sets is an effective instrument in algebra. In this note we drive some basic combinatorial properties of soft groups using Aktas's definition of soft group and soft subgroups. By giving the definition of soft actions of groups and semigroups we managed to exhibit their congruence properties in this paper.

Keywords


Soft set; Soft semigroup; Soft group; Soft subgroup; Soft action; Congruence

Full Text:

PDF

References


H. Aktas, and N. Cogman, Soft Sets and Soft Groups, Information Sciences. 177 (2007) 2726-2735.

Basu, K., Deb, R. and Pattanaik, P. K. : Soft sets: An ordinal formulation of vagueness with

some applications to the theory of choice , Fuzzy Sets and Systems. 45 (1992) 45-58.

H. Aktas, and S. Ozlu, Cyclic soft groups and their applications on groups. The scientific world journal. Vol. 2014. Article ID: 437324. Hindawi Pub. Co.

M. Aslam and S. M. Qurashi, Some Contribution to Soft Groups, Annals of Fuzzy Mathematics and Informatics. 4(1), (2012)177-195.

R. Lin, J. Wang.: Soft homomorphism properties on soft groups and soft normal groups. IEEE International Conference on Granular Computing. (2011).

Maji, P. K., Biswas, R.and Roy, A. R.: Fuzzy Soft Sets, The Journal of Fuzzy Mathematics.

(3) (2001) 677-692.

P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, Computers and Mathematics with

Applications. 45 (2003) 555-562.

D. Molodtsov, Soft set Theory-First results, Computers and Mathematics with Applications.

(1999) 19-31.

A. Sezgin, and A. O. Atagun, Soft groups and normalistic soft groups. Computer and mathematics with Applications. 62 (2011) 685-698.

X. Yin and Z. Liao, Study on soft groups. Journal of Computers. V. 8, No. 4 (2013).

M. Zhou, Zhou, S. Li and M. Akram.: Categorical Properties of Soft Sets. The scientic World Journal. Vol. 2014, Article ID 783056. Hindawi Pub. Co.




DOI: http://dx.doi.org/10.26713%2Fjims.v8i3.401

eISSN 0975-5748; pISSN 0974-875X